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Found 16 papers, 4 papers with code
Persistent Classification: A New Approach to Stability of Data and Adversarial Examples
This article proposes a new framework for studying adversarial examples that does not depend directly on the distance to the decision boundary.
Manifold learning in Wasserstein space
This paper aims at building the theoretical foundations for manifold learning algorithms in the space of absolutely continuous probability measures on a compact and convex subset of $\mathbb{R}^d$, metrized with the Wasserstein-2 distance $W$.
Lattice Approximations in Wasserstein Space
We consider structured approximation of measures in Wasserstein space $W_p(\mathbb{R}^d)$ for $p\in[1,\infty)$ by discrete and piecewise constant measures based on a scaled Voronoi partition of $\mathbb{R}^d$.
On Wasserstein distances for affine transformations of random vectors
We expound on some known lower bounds of the quadratic Wasserstein distance between random vectors in $\mathbb{R}^n$ with an emphasis on affine transformations that have been used in manifold learning of data in Wasserstein space.
Boosting Nyström Method
To improve the standard Nystr\"{o}m approximation, ensemble Nystr\"{o}m algorithms compute a mixture of Nystr\"{o}m approximations which are generated independently based on column resampling.
Linearized Wasserstein dimensionality reduction with approximation guarantees
We introduce LOT Wassmap, a computationally feasible algorithm to uncover low-dimensional structures in the Wasserstein space.
Riemannian CUR Decompositions for Robust Principal Component Analysis
This algorithm has the same computational complexity as Iterated Robust CUR, which is currently state-of-the-art, but is more robust to outliers.
Wassmap: Wasserstein Isometric Mapping for Image Manifold Learning
In this paper, we propose Wasserstein Isometric Mapping (Wassmap), a nonlinear dimensionality reduction technique that provides solutions to some drawbacks in existing global nonlinear dimensionality reduction algorithms in imaging applications.
Computing Steiner Trees using Graph Neural Networks
Graph neural networks have been successful in many learning problems and real-world applications.
On Matrix Factorizations in Subspace Clustering
This article explores subspace clustering algorithms using CUR decompositions, and examines the effect of various hyperparameters in these algorithms on clustering performance on two real-world benchmark datasets, the Hopkins155 motion segmentation dataset and the Yale face dataset.
Mode-wise Tensor Decompositions: Multi-dimensional Generalizations of CUR Decompositions
Low rank tensor approximation is a fundamental tool in modern machine learning and data science.
Multi-level Weighted Additive Spanners
In this paper, we consider a multi-level version of the subsetwise spanner in weighted graphs, where the vertices in $S$ possess varying level, priority, or quality of service (QoS) requirements, and the goal is to compute a nested sequence of spanners with the minimum number of total edges.
Discrete Mathematics
Robust CUR Decomposition: Theory and Imaging Applications
Additionally, we consider hybrid randomized and deterministic sampling methods which produce a compact CUR decomposition of a given matrix, and apply this to video sequences to produce canonical frames thereof.
Rapid Robust Principal Component Analysis: CUR Accelerated Inexact Low Rank Estimation
Robust principal component analysis (RPCA) is a widely used tool for dimension reduction.
CUR Decompositions, Approximations, and Perturbations
This article discusses a useful tool in dimensionality reduction and low-rank matrix approximation called the CUR decomposition.
CUR Decompositions, Similarity Matrices, and Subspace Clustering
An algorithm based on the theoretical construction of similarity matrices is presented, and experiments on synthetic and real data are presented to test the method.
